1. Extinction and persistence of a stochastic SIRV epidemic model with nonlinear incidence rate
- Author
-
Chunxia Wang, Zhidong Teng, and Ramziya Rifhat
- Subjects
Lyapunov function ,Permanence in the mean ,01 natural sciences ,010305 fluids & plasmas ,symbols.namesake ,Stochastic epidemic model ,0103 physical sciences ,92D30 ,Applied mathematics ,Quantitative Biology::Populations and Evolution ,0101 mathematics ,Nonlinear incidence rate ,Mathematics ,60H40 ,Threshold value ,Algebra and Number Theory ,Extinction ,Partial differential equation ,Stochastic process ,Applied Mathematics ,Research ,lcsh:Mathematics ,lcsh:QA1-939 ,010101 applied mathematics ,Ordinary differential equation ,symbols ,60H10 ,Persistence (discontinuity) ,Epidemic model ,Analysis - Abstract
In this paper, a stochastic SIRV epidemic model with general nonlinear incidence and vaccination is investigated. The value of our study lies in two aspects. Mathematically, with the help of Lyapunov function method and stochastic analysis theory, we obtain a stochastic threshold of the model that completely determines the extinction and persistence of the epidemic. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics. In other words, neglecting random perturbations overestimates the ability of the disease to spread. The numerical simulations are given to illustrate the main theoretical results.
- Published
- 2021